Yes especially by using one of the field spectroradiometers and a validation field data; from the soil spectral signatures and the validation data you can fit regression models for each one of the soil characteristics ( linear, multiple linear, standard least square or stepwise selection).
You can not measuring available nutrients - NO3, NH4, P and K directly from satellite and air-born images. You need field validation data and field spectroradiometer data. You can also determine humus content, as well as N total in the soil and clay content based on multyspectral data.